A lower bound for the canonical height on elliptic curves over abelian extensions

Joseph H. Silverman

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A lower bound for the canonical height on elliptic curves over abelian extensions

Joseph H. Silverman

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Abstract

Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prove that there is a positive constant C(E/K) so that every nontorsion point P in E(K^ab) satisfies h(P) > C(E/K).

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Joseph H. Silverman. 2003-05-01. A lower bound for the canonical height on elliptic curves over abelian extensions. https://arxiv.org/abs/math/0305041

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